Multiscale Modeling &Simulation, Volume 19, Issue 3, Page 1190-1211, January 2021.
We study wave propagation in materials in which the refractive index varies in time. We compare the situations in which the variations are periodic and random. If the modulation period (in the periodic case) or the coherence time (in the random case) of the refractive index is much smaller than the central wave period, then the two situations are analogous, and effective dispersion is the main effect. If the modulation period or coherence time is of the same order as the central wave period, then wavenumber-dependent amplification and dispersion are the main effects, but they have different characteristics: the amplification is very narrowband in the periodic case and broadband in the random case. In the random case, we get an analog of the O'Doherty--Anstey theory in randomly spatially varying media: the wave front experiences a random shift and a deterministic deformation, but contrary to the spatially varying case, the deterministic deformation induced by random time variations involves amplification and dispersion; moreover, the incoherent wave fluctuations grow faster than the coherent wave front, so that the former eventually dominate the latter.

中文翻译：

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周期性和随机时间相关介质中的波传播

多尺度建模与仿真，第 19 卷，第 3 期，第 1190-1211 页，2021 年 1 月。
我们研究折射率随时间变化的材料中的波传播。我们比较了周期性和随机变化的情况。如果折射率的调制周期（在周期性情况下）或相干时间（在随机情况下）远小于中心波周期，则两种情况类似，有效色散是主要影响。如果调制周期或相干时间与中心波周期同阶，则波数相关放大和色散是主要效应，但它们具有不同的特点：在周期情况下放大很窄带，在随机情况下放大很宽。案件。在随机情况下，我们在随机空间变化的媒体中得到了 O'Doherty--Anstey 理论的模拟：波前经历随机位移和确定性变形，但与空间变化情况相反，随机时间变化引起的确定性变形涉及放大和色散；而且，非相干波的波动比相干波阵面增长得更快，因此前者最终主导了后者。